3(4^x)=4(5^{2x-7})

解

3 (4^{x}) = 4 (5^{2 x - 7})

x = - \frac{7 ln ( 5 ) + ln ( 3 ) - 2 ln ( 2 )}{2 ( ln ( 2 ) - ln ( 5 ) )}

十進法表記

x = 5.99066 \dots

解答ステップ

3 (4^{x}) = 4 (5^{2 x - 7})

指数の規則を適用する

ln (3) + x ln (4) = ln (4) + (2 x - 7) ln (5)

解く

ln (3) + x ln (4) = ln (4) + (2 x - 7) ln (5) : x = - \frac{7 ln ( 5 ) + ln ( 3 ) - 2 ln ( 2 )}{2 ( ln ( 2 ) - ln ( 5 ) )}

x = - \frac{7 ln ( 5 ) + ln ( 3 ) - 2 ln ( 2 )}{2 ( ln ( 2 ) - ln ( 5 ) )}